You could switch to Waterfox – which is a fork of Firefox made before XUL/XPComm support was removed. Waterfox will keep this support, while also supporting WebExtensions (see also Wikipedia for additional details). As of this writing, Watefox is at v56.* (i.e. one version behind Firefox).
Waterfox is available for Linux, MacOS, Windows and Android. It is also more light-weight than its "parent", having removed several controverse features like Telemetry, Pocket, sponsored tiles. Another pro is it's allowing unsigned Addons (so one is no longer forced to Mozilla's signing).
So let's see how this meets your requirements:
- lightweight browser: compared to Firefox, yes (as some of the bloat has been removed)
- Down Them All: Should work with Waterfox
Migration from Firefox to Waterfox is quite easy: on its first start, it offers to import your settings, bookmarks etc. from "other browsers"; with Firefox it should be a complete import. If that doesn't work out (or, as I experienced it with the portable version, that "Migration assistant" doesn't fire at all), you can simply copy the profile folder from Firefox to replace the one created by Waterfox.
Like Firefox, Waterfox is open source. It has its own Github presence, where you can file any issues you're having (or ask for enhancements; I'd say that's the first address for support). If you're a member of Reddit, Waterfox also has an official SubReddit.
Another option would be Pale Moon, which is another Firefox fork – made as protest to the Australis switch with Firefox 29. With Pale Moon however you would not have WebExtension support; while it's still maintained, for many things it's still at v27 (and yes, that's the version number PM currently carries). Many of the Firefox addons will work with it, many others not, and PM has its own "Addon server" with adapted addons.